Calculating the correct angle needed to bend a plane into a "cylinder shape"
It is just linear, it seems

If it is for N diamonds in the line above, then the angle is:
360 * (1 + 1 / (2 * N))

as we need to fill one half one diamond plus these N.
Or to say it another way, this is the ratio of the size considering the half diamond by the size without it x the angle.